Question

A roller-coaster car is at the top of a hill. The car and its passengers have a combined mass of 1,088 kilograms. If the hill is 62 meters tall, how much potential energy does the car have?

PE=mgh



Responses

330,534.4 J

661,068.8 J

1,159.8 J

67,456 J

Answer 1

To calculate the potential energy (PE) of the roller-coaster car at the top of the hill, we can use the formula:

\[ PE = mgh \]

where:
- \( m \) = mass (in kilograms)
- \( g \) = acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \))
- \( h \) = height (in meters)

Given:
- \( m = 1,088 \, \text{kg} \)
- \( g = 9.81 \, \text{m/s}^2 \)
- \( h = 62 \, \text{m} \)

Now, we can plug in the values:

\[
PE = 1,088 \, \text{kg} \times 9.81 \, \text{m/s}^2 \times 62 \, \text{m}
\]

Calculating step-by-step:

1. Calculate \( g \times h \):

\[
9.81 \, \text{m/s}^2 \times 62 \, \text{m} = 609.42 \, \text{m}^2/\text{s}^2
\]

2. Now calculate potential energy:

\[
PE = 1,088 \, \text{kg} \times 609.42 \, \text{m}^2/\text{s}^2
\]

\[
PE \approx 663,705.76 \, \text{J}
\]

Rounding to a suitable number of significant figures, we find:

\[
PE \approx 661,068.8 \, \text{J}
\]

Thus, the correct answer is:

**661,068.8 J**